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Rounding numbers
THE GAME DID NOT BRING A BREAKTHROUGH
RECORD VIEWS OF THE FINAL GAME
Yesterday's match took place in front of \latex{ 50,000 } fans
and ended in a \latex{ 3 }-\latex{ 2 } victory for Brazil.
and ended in a \latex{ 3 }-\latex{ 2 } victory for Brazil.
Yesterday’s World Cup match was watched
in \latex{ 198 } countries by nearly \latex{ 900 } million viewers.
in \latex{ 198 } countries by nearly \latex{ 900 } million viewers.
The number of goals and the number of countries broadcasting the final game were given exactly.
An approximate number of viewers was provided because an exact number could not be given.
The number of fans in the stadium was given approximately and rounded. The exact number may be known, but it is not important.
When rounding, indicate which place value you are rounding to.
ROUNDING TO TENS
ROUNDING TO HUNDREDS
Round down if the ones are
\latex{ 0 }, \latex{ 1 }, \latex{ 2 }, \latex{ 3 } or \latex{ 4 }.
The number in the tens is unchanged,
the ones are replaced by \latex{ 0 }.
\latex{ 0 }, \latex{ 1 }, \latex{ 2 }, \latex{ 3 } or \latex{ 4 }.
The number in the tens is unchanged,
the ones are replaced by \latex{ 0 }.
Round down if the tens are
\latex{ 0 }, \latex{ 1 }, \latex{ 2 }, \latex{ 3 } or \latex{ 4 }.
The number in the hundreds is unchanged,
and the ones and the tens are replaced by \latex{ 0 }.
\latex{ 0 }, \latex{ 1 }, \latex{ 2 }, \latex{ 3 } or \latex{ 4 }.
The number in the hundreds is unchanged,
and the ones and the tens are replaced by \latex{ 0 }.
Round up if the ones are
\latex{ 5 }, \latex{ 6 }, \latex{ 7 }, \latex{ 8 } or \latex{ 9 }.
Increase the number in the tens by one,
and replace the ones with \latex{ 0 }.
\latex{ 5 }, \latex{ 6 }, \latex{ 7 }, \latex{ 8 } or \latex{ 9 }.
Increase the number in the tens by one,
and replace the ones with \latex{ 0 }.
Round up if the tens are
\latex{ 5 }, \latex{ 6 }, \latex{ 7 }, \latex{ 8 } or \latex{ 9 }.
Increase the number in the hundreds by one,
and replace the tens and the ones with \latex{ 0 }.
\latex{ 5 }, \latex{ 6 }, \latex{ 7 }, \latex{ 8 } or \latex{ 9 }.
Increase the number in the hundreds by one,
and replace the tens and the ones with \latex{ 0 }.
€\latex{ 19 }
€\latex{ 16 }
€\latex{ 20 }
€\latex{ 70 }
€\latex{ 71 }
€\latex{ 31 }
€\latex{ 7 }
Example 1
How many natural numbers are there that approximate to
a) \latex{ 50 } when rounded to the nearest ten;
b) \latex{ 400 } when rounded to the nearest hundred?
Solution
a) The numbers are: \latex{ 45 }, \latex{ 46 }, \latex{ 47 }, \latex{ 48 }, \latex{ 49 }, \latex{ 50 }, \latex{ 51 }, \latex{ 52 }, \latex{ 53 }, \latex{ 54 }. There are \latex{ 10 } numbers that round to \latex{ 50 } when rounded to the nearest ten.
\latex{ 45 }
\latex{ 50 }
\latex{ 55 }
b) The smallest number that rounds up to \latex{ 400 } is \latex{ 350 }, and the largest number that rounds down to \latex{ 400 } is \latex{ 449 }. There are \latex{ 100 } natural numbers between \latex{ 350 } and \latex{ 449 } (including the numbers themselves).
\latex{ 350 }
\latex{ 400 }
\latex{ 450 }
The rounding error
The rounding error is the difference between the rounded value and the exact value.
Example 2
What is the rounding error when we round \latex{ 1,746 } to the nearest ten, hundred and thousand?
Rounded value
Number line
Rounding
error
error
\latex{1,746 ≈ 1,750}
\latex{1,746 ≈ 1,700}
\latex{1,746 ≈ 2,000}
\latex{1,740}
\latex{1,746}
\latex{1,750}
\latex{1,750 - 1,746 = \textbf{4}}
\latex{1,746 – 1,700 = \textbf{46}}
\latex{2,000 – 1,746 = \textbf{254}}
\latex{1,700}
\latex{1,746}
\latex{1,800}
\latex{1,000}
\latex{1,746}
\latex{2,000}
\latex{\textbf{4}}
\latex{\textbf{46}}
\latex{\textbf{254}}
tens:
hundreds:
thousands:
Exercises
{{exercise_number}}. Researchers have observed blue whales that are approximately \latex{ 33 } \latex{ metres } long and weigh around \latex{ 145 } \latex{ tonnes }. What are the minimum and maximum weight and height of such a whale?
{{exercise_number}}. Rob is approximately \latex{ 130\,cm } tall. How tall can he be exactly?
{{exercise_number}}. Which natural numbers...
a) round to \latex{ 70 } when rounded to the nearest ten;
b) round to \latex{ 200 } when rounded to the nearest hundred;
c) round to \latex{ 5,000 } when rounded to the nearest thousand;
d) round to \latex{ 8,000 } when rounded to the nearest hundred?
b) round to \latex{ 200 } when rounded to the nearest hundred;
c) round to \latex{ 5,000 } when rounded to the nearest thousand;
d) round to \latex{ 8,000 } when rounded to the nearest hundred?
Make a number line for each question. How many numbers are there? What is the largest rounding error?
{{exercise_number}}. Round the following numbers to the nearest ten and hundred. What is the rounding error for each?
a) \latex{ 3,748 }
b) \latex{ 701 }
c) \latex{ 3,196 }
d) \latex{ 9,572 }
e) \latex{ 374 }
f) \latex{ 7,007 }
g) \latex{ 3,106 }
h) \latex{ 9,527 }
i) \latex{ 37 }
j) \latex{ 7,117 }
k) \latex{ 5,996 }
l) \latex{ 9,752 }
{{exercise_number}}. Round the following numbers to the nearest thousand and ten thousand. What is the rounding error in each case?
a) \latex{ 5,555 }
b) \latex{ 30,034 }
c) \latex{ 40,009 }
d) \latex{ 71,518 }
e) \latex{ 6,666 }
f) \latex{ 30,909 }
g) \latex{ 40,199 }
h) \latex{ 79,658 }
i) \latex{ 9,999 }
j) \latex{ 39,997 }
k) \latex{ 40,789 }
l) \latex{ 79,095 }
{{exercise_number}}. Which of the following numbers is the rounded form of \latex{ 12,568 }?
A: \latex{ 12,560 }
B: \latex{ 12,500 }
C: \latex{ 12,600 }
D: \latex{ 12,570 }
E: \latex{ 12,580 }
F: \latex{ 13,000 }
G: \latex{ 10,000 }
{{exercise_number}}. The image shows the population of four English towns in \latex{ 2001 }. Each human figure represents \latex{ 10,000 } people. How many people can live in each of these towns?
Rugby
Chelmsford
Scarborough
Luton
Quiz
When rounding \latex{ 2,004 } to the nearest thousand, the last three digits of the number are zero. How many four-digit natural numbers can be rounded in the same way?
